Skillnad mellan versioner av "2.3a Lösning 8a"

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(Skapade sidan med ':<math> f(x+h) = (x+h)^3 = (x+h) \cdot (x+h)^2 = (x+h) \cdot (x^2 + 2\,x\,h + h^2) = x^3 + 2\,x^2\,h + x\,h^2 + x^2\,h + 2\,x\,h^2 + h^3 = </math> ::<math> \lim_{h \to 0}\,\...')
 
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Rad 1: Rad 1:
:<math> f(x+h) = (x+h)^3 = (x+h) \cdot (x+h)^2 = (x+h) \cdot (x^2 + 2\,x\,h + h^2) = x^3 + 2\,x^2\,h + x\,h^2 + x^2\,h + 2\,x\,h^2 + h^3 = </math>
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:<math> \begin{array}{rcl} f(x+h) & = & (x+h)^3 = (x+h) \cdot (x+h)^2 = (x+h) \cdot (x^2 + 2\,x\,h + h^2) = \\
 
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                                  & = & x^3 + 2\,x^2\,h + x\,h^2 + x^2\,h + 2\,x\,h^2 + h^3 =  
::<math> \lim_{h \to 0}\,\,{f(x+h) - f(x) \over h} = \lim_{h \to 0} {(x+h)^2 - x^2 \over h} = \lim_{h \to 0} {x^2 + 2\,x\,h + h^2 \, - \, x^2 \over h} = \lim_{h \to 0} {2\,x\,h + h^2 \over h} = </math>
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\end{array}</math>
 
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::<math> = \lim_{h \to 0} {{\color{Red} h}\,(2\,x + h) \over {\color{Red} h}} = \lim_{h \to 0} \, (2\,x + h) =  2\,x </math>
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Versionen från 28 september 2014 kl. 21.18

\[ \begin{array}{rcl} f(x+h) & = & (x+h)^3 = (x+h) \cdot (x+h)^2 = (x+h) \cdot (x^2 + 2\,x\,h + h^2) = \\ & = & x^3 + 2\,x^2\,h + x\,h^2 + x^2\,h + 2\,x\,h^2 + h^3 = \end{array}\]